INFLUENCE OF THE VELOCITY-GRADIENT ON THE STAGNATION POINT BEATING INHYPERSONIC FLOW

In a number of experimental and numerical publications a deviation has been found between the measured or computed stagnation point heat flu x and that given by the theory of Fay and Riddell. Since the formula o f Fay and Riddell is used in many applications to yield a reference he at flux for experiments performed in wind tunnels, for flight testing and numerical simulations, it is important that this reference heat fl ux is as accurate as possible. There are some shortcomings in experime nts and numerical Simulations which are responsible in some part for t he deviations observed. But, as will be shown in the present paper, th ere is also a shortcoming on the theoretical side which plays a major role in the deviation between the theoretical and experimental/numeric al stagnation point heat fluxes. This is caused by the method used so far to determine the tangential velocity gradient at the stagnation po int. This value is important for the stagnation point heat flux, which so far has been determined by a simple Newtonian flow model. In the p resent paper a new expression for the tangential velocity gradient is derived, which is based on a more realistic flow model. An integral me thod is used to solve the conservation equations and, for the stagnati on point, yields an explicit solution of the tangential velocity gradi ent. The solution achieved is also valid for high temperature flows wi th real gas effects. A comparison of numerical and experimental result s shows good agreement with the stagnation point heat flux according t o the theory of Fay and Riddell, if the tangential velocity gradient i s determined by the new theory presented in this paper.